Kwantyle rozkładu χ2 |
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α |
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k |
0,999 |
0,99 |
0,98 |
0,97 |
0,96 |
0,95 |
0,94 |
0,93 |
0,92 |
0,91 |
0,90 |
0,80 |
0,70 |
0,60 |
0,50 |
0,40 |
0,30 |
0,20 |
0,10 |
0,09 |
0,08 |
0,07 |
0,06 |
0,05 |
0,04 |
0,03 |
0,02 |
0,01 |
0,001 |
1 |
0,000002 |
0,000157 |
0,000628 |
0,001414 |
0,002515 |
0,003932 |
0,005666 |
0,007717 |
0,010087 |
0,012778 |
0,015791 |
0,064185 |
0,148 |
0,275 |
0,455 |
0,708 |
1,074 |
1,642 |
2,706 |
2,874 |
3,065 |
3,283 |
3,537 |
3,841 |
4,218 |
4,709 |
5,412 |
6,635 |
10,827 |
2 |
0,002 |
0,020 |
0,040 |
0,061 |
0,082 |
0,103 |
0,124 |
0,145 |
0,167 |
0,189 |
0,211 |
0,446 |
0,713 |
1,022 |
1,386 |
1,833 |
2,408 |
3,219 |
4,605 |
4,816 |
5,051 |
5,319 |
5,627 |
5,991 |
6,438 |
7,013 |
7,824 |
9,210 |
13,815 |
3 |
0,024 |
0,115 |
0,185 |
0,245 |
0,300 |
0,352 |
0,401 |
0,449 |
0,495 |
0,540 |
0,584 |
1,005 |
1,424 |
1,869 |
2,366 |
2,946 |
3,665 |
4,642 |
6,251 |
6,491 |
6,759 |
7,060 |
7,407 |
7,815 |
8,311 |
8,947 |
9,837 |
11,345 |
16,266 |
4 |
0,091 |
0,297 |
0,429 |
0,535 |
0,627 |
0,711 |
0,788 |
0,862 |
0,931 |
0,999 |
1,064 |
1,649 |
2,195 |
2,753 |
3,357 |
4,045 |
4,878 |
5,989 |
7,779 |
8,043 |
8,337 |
8,666 |
9,044 |
9,488 |
10,026 |
10,712 |
11,668 |
13,277 |
18,466 |
5 |
0,210 |
0,554 |
0,752 |
0,903 |
1,031 |
1,145 |
1,250 |
1,347 |
1,439 |
1,526 |
1,610 |
2,343 |
3,000 |
3,656 |
4,351 |
5,132 |
6,064 |
7,289 |
9,236 |
9,521 |
9,837 |
10,191 |
10,596 |
11,070 |
11,644 |
12,375 |
13,388 |
15,086 |
20,515 |
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6 |
0,381 |
0,872 |
1,134 |
1,330 |
1,492 |
1,635 |
1,765 |
1,885 |
1,997 |
2,103 |
2,204 |
3,070 |
3,828 |
4,570 |
5,348 |
6,211 |
7,231 |
8,558 |
10,645 |
10,948 |
11,283 |
11,660 |
12,090 |
12,592 |
13,198 |
13,968 |
15,033 |
16,812 |
22,457 |
7 |
0,599 |
1,239 |
1,564 |
1,802 |
1,997 |
2,167 |
2,320 |
2,461 |
2,592 |
2,716 |
2,833 |
3,822 |
4,671 |
5,493 |
6,346 |
7,283 |
8,383 |
9,803 |
12,017 |
12,337 |
12,691 |
13,088 |
13,540 |
14,067 |
14,703 |
15,509 |
16,622 |
18,475 |
24,321 |
8 |
0,857 |
1,647 |
2,032 |
2,310 |
2,537 |
2,733 |
2,908 |
3,068 |
3,217 |
3,357 |
3,490 |
4,594 |
5,527 |
6,423 |
7,344 |
8,351 |
9,524 |
11,030 |
13,362 |
13,697 |
14,068 |
14,484 |
14,956 |
15,507 |
16,171 |
17,011 |
18,168 |
20,090 |
26,124 |
9 |
1,152 |
2,088 |
2,532 |
2,848 |
3,105 |
3,325 |
3,521 |
3,700 |
3,866 |
4,021 |
4,168 |
5,380 |
6,393 |
7,357 |
8,343 |
9,414 |
10,656 |
12,242 |
14,684 |
15,034 |
15,421 |
15,854 |
16,346 |
16,919 |
17,608 |
18,480 |
19,679 |
21,666 |
27,877 |
10 |
1,479 |
2,558 |
3,059 |
3,412 |
3,697 |
3,940 |
4,157 |
4,353 |
4,535 |
4,705 |
4,865 |
6,179 |
7,267 |
8,295 |
9,342 |
10,473 |
11,781 |
13,442 |
15,987 |
16,352 |
16,753 |
17,203 |
17,713 |
18,307 |
19,021 |
19,922 |
21,161 |
23,209 |
29,588 |
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11 |
1,834 |
3,053 |
3,609 |
3,997 |
4,309 |
4,575 |
4,810 |
5,024 |
5,221 |
5,405 |
5,578 |
6,989 |
8,148 |
9,237 |
10,341 |
11,530 |
12,899 |
14,631 |
17,275 |
17,653 |
18,069 |
18,533 |
19,061 |
19,675 |
20,412 |
21,342 |
22,618 |
24,725 |
31,264 |
12 |
2,214 |
3,571 |
4,178 |
4,601 |
4,939 |
5,226 |
5,480 |
5,710 |
5,921 |
6,118 |
6,304 |
7,807 |
9,034 |
10,182 |
11,340 |
12,584 |
14,011 |
15,812 |
18,549 |
18,939 |
19,369 |
19,849 |
20,393 |
21,026 |
21,785 |
22,742 |
24,054 |
26,217 |
32,909 |
13 |
2,617 |
4,107 |
4,765 |
5,221 |
5,584 |
5,892 |
6,163 |
6,409 |
6,634 |
6,844 |
7,041 |
8,634 |
9,926 |
11,129 |
12,340 |
13,636 |
15,119 |
16,985 |
19,812 |
20,214 |
20,657 |
21,151 |
21,711 |
22,362 |
23,142 |
24,125 |
25,471 |
27,688 |
34,527 |
14 |
3,041 |
4,660 |
5,368 |
5,856 |
6,243 |
6,571 |
6,859 |
7,120 |
7,359 |
7,581 |
7,790 |
9,467 |
10,821 |
12,078 |
13,339 |
14,685 |
16,222 |
18,151 |
21,064 |
21,478 |
21,933 |
22,441 |
23,017 |
23,685 |
24,485 |
25,493 |
26,873 |
29,141 |
36,124 |
15 |
3,483 |
5,229 |
5,985 |
6,503 |
6,914 |
7,261 |
7,566 |
7,841 |
8,093 |
8,327 |
8,547 |
10,307 |
11,721 |
13,030 |
14,339 |
15,733 |
17,322 |
19,311 |
22,307 |
22,732 |
23,199 |
23,720 |
24,311 |
24,996 |
25,816 |
26,848 |
28,259 |
30,578 |
37,698 |
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16 |
3,942 |
5,812 |
6,614 |
7,163 |
7,596 |
7,962 |
8,283 |
8,572 |
8,836 |
9,082 |
9,312 |
11,152 |
12,624 |
13,983 |
15,338 |
16,780 |
18,418 |
20,465 |
23,542 |
23,977 |
24,456 |
24,990 |
25,595 |
26,296 |
27,136 |
28,191 |
29,633 |
32,000 |
39,252 |
17 |
4,416 |
6,408 |
7,255 |
7,832 |
8,288 |
8,672 |
9,008 |
9,311 |
9,588 |
9,845 |
10,085 |
12,002 |
13,531 |
14,937 |
16,338 |
17,824 |
19,511 |
21,615 |
24,769 |
25,215 |
25,705 |
26,251 |
26,870 |
27,587 |
28,445 |
29,523 |
30,995 |
33,409 |
40,791 |
18 |
4,905 |
7,015 |
7,906 |
8,512 |
8,989 |
9,390 |
9,742 |
10,058 |
10,347 |
10,614 |
10,865 |
12,857 |
14,440 |
15,893 |
17,338 |
18,868 |
20,601 |
22,760 |
25,989 |
26,445 |
26,947 |
27,505 |
28,137 |
28,869 |
29,745 |
30,845 |
32,346 |
34,805 |
42,312 |
19 |
5,407 |
7,633 |
8,567 |
9,200 |
9,698 |
10,117 |
10,483 |
10,812 |
11,112 |
11,391 |
11,651 |
13,716 |
15,352 |
16,850 |
18,338 |
19,910 |
21,689 |
23,900 |
27,204 |
27,669 |
28,181 |
28,751 |
29,396 |
30,144 |
31,037 |
32,158 |
33,687 |
36,191 |
43,819 |
20 |
5,921 |
8,260 |
9,237 |
9,897 |
10,415 |
10,851 |
11,231 |
11,573 |
11,884 |
12,173 |
12,443 |
14,578 |
16,266 |
17,809 |
19,337 |
20,951 |
22,775 |
25,038 |
28,412 |
28,887 |
29,410 |
29,991 |
30,649 |
31,410 |
32,321 |
33,462 |
35,020 |
37,566 |
45,314 |
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21 |
6,447 |
8,897 |
9,915 |
10,601 |
11,140 |
11,591 |
11,986 |
12,339 |
12,662 |
12,961 |
13,240 |
15,445 |
17,182 |
18,768 |
20,337 |
21,992 |
23,858 |
26,171 |
29,615 |
30,100 |
30,632 |
31,225 |
31,895 |
32,671 |
33,597 |
34,759 |
36,343 |
38,932 |
46,796 |
22 |
6,983 |
9,542 |
10,600 |
11,313 |
11,870 |
12,338 |
12,746 |
13,112 |
13,445 |
13,753 |
14,041 |
16,314 |
18,101 |
19,729 |
21,337 |
23,031 |
24,939 |
27,301 |
30,813 |
31,307 |
31,849 |
32,453 |
33,135 |
33,924 |
34,867 |
36,049 |
37,659 |
40,289 |
48,268 |
23 |
7,529 |
10,196 |
11,293 |
12,030 |
12,607 |
13,091 |
13,512 |
13,889 |
14,233 |
14,551 |
14,848 |
17,187 |
19,021 |
20,690 |
22,337 |
24,069 |
26,018 |
28,429 |
32,007 |
32,510 |
33,062 |
33,675 |
34,370 |
35,172 |
36,131 |
37,332 |
38,968 |
41,638 |
49,728 |
24 |
8,085 |
10,856 |
11,992 |
12,754 |
13,350 |
13,848 |
14,283 |
14,672 |
15,026 |
15,353 |
15,659 |
18,062 |
19,943 |
21,652 |
23,337 |
25,106 |
27,096 |
29,553 |
33,196 |
33,708 |
34,269 |
34,893 |
35,599 |
36,415 |
37,389 |
38,609 |
40,270 |
42,980 |
51,179 |
25 |
8,649 |
11,524 |
12,697 |
13,484 |
14,098 |
14,611 |
15,059 |
15,459 |
15,823 |
16,159 |
16,473 |
18,940 |
20,867 |
22,616 |
24,337 |
26,143 |
28,172 |
30,675 |
34,382 |
34,902 |
35,472 |
36,106 |
36,824 |
37,652 |
38,642 |
39,880 |
41,566 |
44,314 |
52,619 |
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26 |
9,222 |
12,198 |
13,409 |
14,219 |
14,851 |
15,379 |
15,839 |
16,250 |
16,624 |
16,970 |
17,292 |
19,820 |
21,792 |
23,579 |
25,336 |
27,179 |
29,246 |
31,795 |
35,563 |
36,091 |
36,671 |
37,315 |
38,044 |
38,885 |
39,889 |
41,146 |
42,856 |
45,642 |
54,051 |
27 |
9,803 |
12,878 |
14,125 |
14,959 |
15,609 |
16,151 |
16,624 |
17,045 |
17,429 |
17,783 |
18,114 |
20,703 |
22,719 |
24,544 |
26,336 |
28,214 |
30,319 |
32,912 |
36,741 |
37,278 |
37,866 |
38,520 |
39,259 |
40,113 |
41,132 |
42,407 |
44,140 |
46,963 |
55,475 |
28 |
10,391 |
13,565 |
14,847 |
15,704 |
16,371 |
16,928 |
17,412 |
17,844 |
18,238 |
18,601 |
18,939 |
21,588 |
23,647 |
25,509 |
27,336 |
29,249 |
31,391 |
34,027 |
37,916 |
38,460 |
39,058 |
39,721 |
40,471 |
41,337 |
42,370 |
43,662 |
45,419 |
48,278 |
56,892 |
29 |
10,986 |
14,256 |
15,574 |
16,454 |
17,138 |
17,708 |
18,204 |
18,647 |
19,050 |
19,421 |
19,768 |
22,475 |
24,577 |
26,475 |
28,336 |
30,283 |
32,461 |
35,139 |
39,087 |
39,640 |
40,246 |
40,919 |
41,679 |
42,557 |
43,604 |
44,913 |
46,693 |
49,588 |
58,301 |
30 |
11,588 |
14,953 |
16,306 |
17,208 |
17,908 |
18,493 |
19,000 |
19,453 |
19,865 |
20,245 |
20,599 |
23,364 |
25,508 |
27,442 |
29,336 |
31,316 |
33,530 |
36,250 |
40,256 |
40,816 |
41,430 |
42,113 |
42,883 |
43,773 |
44,834 |
46,160 |
47,962 |
50,892 |
59,702 |